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Last Lecture Everything you need to know about dynamics of rotation TodayPowerPoint Presentation

Last Lecture Everything you need to know about dynamics of rotation Today

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- Last Lecture
- Everything you need to know about dynamics of rotation

- Today
- Pendulums and Kinetic Energy of rotation

- Important Concepts
- Equations for angular motion are mostly identical to those for linear motion with the names of the variables changed.
- Kinetic energy of rotation adds a new term to the same energy equation, it does not add a new equation.
- Kinetic energy can be simply written as a linear term and a rotational term

8.01L IAP 2007

Important Reminders

- Note that tutors have both assigned and open sessions this week. See web for schedule
- Mastering Physics due tomorrow at 10pm.
- Experiment in class on Thursday.
- Note that if you do NOT do the necessary calculations in advance, there is a good chance that you will NOT be able to finish the experiment in time.

- Problems-solving in recitation this Friday.
- Pset due this Friday at 4:30pm.

8.01L IAP 2007

Right-Hand-Rule Review (by request)

- Except for the gyroscope, all 8.01L problems can be solved without using R-H-R, use CW/CCW instead.
- However, many problems in 8.02 require R-H-R

- The vector for any angular quantity (, , , , J) points along the axis with the direction given by:
- Fingers curl in direction of , , , , J, thumb points in the direction of the vector

- Cross-product Right-Hand-Rule: Fingers point along vector A, curl fingers to point along vector B, thumb points in direction C.

8.01L IAP 2007

Pendulums

- Simple pendulum: Small mass at the end of a string
- Period is where l is the length from the pivot to the center of the object.

- Physical pendulum: More complex object rotating about any pivot
- Period is where l is the distance from the pivot to the center of mass of the object, M is the total mass, and I is the moment of inertia around the pivot.

8.01L IAP 2007

c.m.

Axis 1

Parallel Axis Theorum- Very simple way to find moment of inertia for a large number of strange axis locations.
- I1 = Ic.m. + Md2 where M is the total mass.

8.01L IAP 2007

Kinetic Energy with Rotation

- Adds a new term not a new equation!
- Rotation around any fixed pivot:
- Moving and rotating:

8.01L IAP 2007

Everything you need to know for Linear & Rotational Dynamics Rolling without slipping: Rolling with slipping:

- This is true for anyfixed axis and for an axis through the center of mass, even if the object moves or accelerates.

- Friction does NOT do work!

- Friction does work, usually negative.
- Rarely solvable without using force and torque equations!

8.01L IAP 2007

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